Non-woven structures are a ubiquitous part of daily life. Non-woven structures are used for cleaning surfaces, such as glass and ceramic tile, and for cleaning the skin of children and adults. Pre-moistened, or wet, non-woven structures are also well known. One aspect of non-woven structures currently in use is the relatively high strength of the wet structures at the time of disposal of the soiled structure. This high strength precludes flushing the wipe into the sewage stream without the risk of clogging the system. A wet structure that has sufficient strength to accomplish the intended cleaning task, and which has a reduced strength upon being disposed is desired.